When using document command arguments for case distinctions I routinely have been using the \str_case:nn function, which works fine as is evident from the output of the \myStrCase command. When attempting to use the \tl_case:Nn function instead, by loading the argument into a _tl type variable, things go miserably wrong. The variable seems to be loaded with the correct value, and is then flagged as correct as far as the \tl_case:Nn function is concerned, but the corresponding code is not executed. Why?

\tl_new:N \l_rn_Aux_tl
    \str_case:nnTF {#1}
  }  %  \myStrCase
    \tl_set:Nx \l_rn_Aux_tl {#1}
checking~what~was~passed:~\l_rn_Aux_tl \\
    \tl_case:NnTF \l_rn_Aux_tl
        emph {\textit{#2}}
        Emph {\textbf{\textit{#2}}}
        uline {\underline{#2}}
  }  %  \myTlCase
\subsection{using str\_case:}
  \myStrCase{Hi There}\\
  \myStrCase[emph]{Hi There}\\
  \myStrCase[Emph]{Hi There}\\
  \myStrCase[uline]{Hi There}\\
  \myStrCase[xxx]{Hi There}
\subsection{using tl\_case:}
  \myTlCase[emph]{Hi There}\\
  \myTlCase[xxx]{Hi There}

The documentation (interface3) already contains your answer:

\tl_case:NnTF <test token list variable>
<token list variable case1> {<code case1>}
<token list variable case2> {<code case2>}
<token list variable casen> {<code casen>}
{<true code>}
{<false code>}

You will find "token list variable" and not "token list" therein. Hence you are asked to provide one token (a variable/N-type argument). So to use this construction you would need to save your options into variables and use these within \tl_case.

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